Normally, the mother dog will severe the cord herself. If she hasn't, then it will become your task.
It is best to keep it a bit longer than too short. Many breeders prefer about 2-3 inches away from the pup's belly.
You will, therefore, have to clamp the cord between puppy and mom with dental floss very tight and then clamp again in a second place leaving at least a couple of inches between where the cord is clamped.
Next, you need to cut the umbilical cord right in between the clamped areas using sterile scissors or even better, thinning shears.
You will then dip the cord in betadine solution and then some clotting powder such as the one used to clot blood when accidentally cutting a dog's nails through the quick. Remove the clamps.